Silicon-on-Insulator (SOI) micro-ring resonators (MRRs) are versatile elements in high-density integrated optics telecommunication systems. However, small inaccuracies in the fabrication process intensely deteriorate the response of SOI MRRs. By utilizing the racetrack resonator structures with strong coupling abilities, one can improve the fabrication tolerance. For the SOI racetrack resonators, the FSR is usually large. By introducing gratings into SOI racetrack resonators, the mutual mode coupling between the clockwise and counterclockwise modes can be induced and result in the resonance splitting. The grating-assisted SOI racetrack resonators can increase the operation wavelength and open up the possibility to overcome this limitation. In this thesis, we first use the 2-D FDTD method with the effective index method (EIM) to obtain the transmission spectra of the SOI racetrack resonators. The transmission spectra are then fitted by using the time-domain coupled mode theory (CMT) to obtain the quality factor and optical parameters of the SOI racetrack resonators. Next, we demonstrate the characteristics of mode splitting resulted from the mutual mode coupling between the clockwise and counterclockwise modes in the grating-assisted racetrack resonators by utilizing both the CMT and the 2-D FDTD method with the EIM. By tuning the grating configurations, such as the length or the structure of sidewall gratings, one can obtain the desired transmission spectrum of the grating-assisted racetrack resonators. Finally, we numerically investigate the temperature-dependent spectral characterics of the grating-assisted SOI racetrack resonator by taking the thermal-optic responce of the SOI materials into account. The thermal sensitivity of this device is 95.38 pm/¢XC, and the calculted properties can help the further designs based on the grating-assisted SOI racetrack resonators.

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